Question

LOUISIANA 4. Assume that during Fall Break, you played - and won! -the lottery. The Lottery Commission people have given you 8 different options regarding how you receive your winnings. Your required return on all investments is 8% and all of the cash flows are after tax cash flows. Which of the 8 following options should you choose? (A) $7,500,000 in cash today (B) $75,000,000 in cash in 30 years (C) $600,000 a year forever, with the first payment in 1 year (D) (E) $550,000 a year forever, with the first payment today $1,000,000 a year forever, with the first payment in 8 years $1,000,000 a year for 12 years, with the first payment in 1 year $1,000,000 a year for 12 years, with the first payment today (12 payments, not 13) $1,000,000 a year for 30 years, with the first payment in 5 years (G) (H) Yes, you can use the most important formula in finance for all of these questions: Present Value = PV = Future Value = FV (1+r)

Answer 1

Option	A
Interest	8%
PV of cash	$            7,500,000.00
Option	B
Payment	$          75,000,000.00
Payment year	30
Interest	8%
PV today	75000000/(1+8%)^30
PV today	$            7,453,299.94
Option	C
Payment	$               600,000.00
Payment year	Forever
First payment	year 1
Interest	8%
PV today	600000/8%
PV today	$            7,500,000.00
Option	D
Payment	$               550,000.00
Payment year	Forever
First payment	year 0
Interest	8%
PV today	550000+550000/8%
PV today	$            7,425,000.00
Option	E
Payment	$            1,000,000.00
Payment year	Forever
First payment	year 8
Interest	8%
PV at year 7=	1000000/8%
PV at year 7=	$          12,500,000.00
PV today	12500000/(1+8%)^7
PV today	$            7,293,629.94
Option	F
Payment	$            1,000,000.00
Payment year	for 12 year
First payment	year 1
Interest	8%
PV today	P = PMT x (((1-(1 + r) ^- n)) / r)
	Where:
	P = the present value of an annuity stream
	PMT = the dollar amount of each annuity payment
	r = the effective interest rate (also known as the discount rate)
	n = the number of periods in which payments will be made
PV today	=1000000* (((1-(1 + 8%) ^- 12)) / 8%)
PV today	$            7,536,078.02
Option	G
Payment	$            1,000,000.00
Payment year	for 12 year
First payment	year 0
Interest	8%
PV today	P = PMT+PMT x (((1-(1 + r) ^- (n-1))) / r)
	Where:
	P = the present value of an annuity stream
	PMT = the dollar amount of each annuity payment
	r = the effective interest rate (also known as the discount rate)
	n = the number of periods in which payments will be made
PV today	=1000000+1000000* (((1-(1 + 8%) ^- (12-1))) / 8%)
PV today	$            8,138,964.26
Option	H
Payment	$            1,000,000.00
Payment year	for 30 year
First payment	year 5
Interest	8%
PV today	P = PMT x (((1-(1 + r) ^- n)) / r)
	Where:
	P = the present value of an annuity stream
	PMT = the dollar amount of each annuity payment
	r = the effective interest rate (also known as the discount rate)
	n = the number of periods in which payments will be made
PV at year 4	=1000000* (((1-(1 + 8%) ^- 30)) / 8%)
PV at year 4	$          11,257,783.34
PV today=	11257783.34/(1+8%)^4
PV today=	$            8,274,806.83
Options	PV	Rank
A	$            7,500,000.00
B	$            7,453,299.94
C	$            7,500,000.00
D	$            7,425,000.00
E	$            7,293,629.94
F	$            7,536,078.02
G	$            8,138,964.26
H	$            8,274,806.83	1
As we can see that the PV is highest in option H and hence this option should be selected